Positive energy-momentum theorem in asymptotically anti de Sitter space-times

TL;DR

This paper establishes a positive energy-momentum theorem for 3-manifolds asymptotic to anti de Sitter space, using spinorial methods, and proves a rigidity result linking degeneracy to isometric embedding.

Contribution

It extends the positive energy-momentum theorem to asymptotically anti de Sitter spaces using spinorial techniques and introduces a rigidity theorem for degenerate cases.

Findings

Proves positive energy-momentum theorem in asymptotically anti de Sitter space.

Establishes a rigidity theorem for degenerate energy-momentum cases.

Uses spinorial methods similar to Witten's proof in flat space.

Abstract

This paper proves a positive energy-momentum theorem for oriented Riemannian 3-manifolds that are asymptotic to a standard hyperbolic slice in anti de Sitter space-time. Analogously to the original Witten's proof in the asymptotically flat case, this result relies on spinorial methods. We also give a rigidity theorem: if the energy-momentum is degenerate (in a certain sense) then our 3-manifold can be isometrically embedded in anti de Sitter.